@Bleistivt thank you very much for the guidance. I got it working. This is what I did, leaving a trail for others to do similarly.

1) Right, I use Pockets, that much is a given.

2) On my website, I use a small paid ChatBox/Shoutbox solution which I have displayed in the right side panel. This is because there is no native Vanilla solution anymore.

3) I use the Bootstrap theme, Darkly option.

My goal: to make the ChatBox only visible to signed-in members, and not to Guests nor Applicants. It still needs to be visible in the right-side panel, but disappear when members sign out.

Steps to remediate:

1) Find the code to use:

{if $User.SignedIn}
{pocket name="Cbox"}
{/if}

2) The theme tpl to use. In my case:

themes/Bootstrap/views/default-master.tpl

3) The Pocket (Cbox) was already created (mostly an iframe driven piece of code). The key is to set it to Custom (not panel). Custom will allow the Pocket to appear/disappear, while if set to Panel, it will be fixed, which is not what we want.

With that information in place, we needed to insert the code into the appropriate part of the tpl file, namely the right-side panel called <aside class="page-sidebar". This was the area in my template to be changed: